On Sunday, Renzi said he would resign following a "clear" rejection of legislative reform measures as what was originally a rather dry referendum on constitutional change turned into a high-stakes game with the political and economic stability of Italy—and ultimately the euro zone—at risk.

"We know that the referendum was technically on constitutional reforms but the Italian government linked the vote to its own political future," said Stratfor's senior European analyst, Adriano Bosoni.

Sunday's vote was on whether the country's second chamber should be stripped of some of its powers. The country's government is hamstrung by procedure and delays to legislation. A "yes" vote in the referendum would have meant that laws would only need the approval of the lower house to be passed.

Renzi had pinned his political future on the vote, saying he would resign if a "yes" vote was rejected.

Italian Prime Minister Matteo Renzi give a speech after the results of the referendum on constitutional reforms at Palazzo Chigi on December 5, 2016 in Rome, Italy. The result of the government referendum that could change the constitution is considered crucial for the political future of Italy and for the personal future of its Prime Minister.

Franco Origlia | Getty Images

While the vote would weigh on Italy's sovereign debt, the impact would likely be contained with aid from the European Central Bank, said Bosoni.

What is more significant about Italy's rejection of the constitutional changes are concerns over its impact on the future of the European Union and euro zone, particularly after the shock outcomes from this year's polls, including the U.K.'s vote to leave the European Union. Also weighing on the political scene is the surprise U.S. election of Donald Trump in a populist wave.

With Renzi leaving, Italy likely faces early elections next year, raising the prospect of a a new political combination in power.

"If you take a look at the political environment in Italy, Renzi's center-left Democratic Party is probably the only mainstream party that still supports the EU and the euro zone," Stratfor's Bosoni told CNBC's "The Rundown". Most of the rest of the top five most popular parties all criticize the trade bloc, he noted.

"Renzi thought he could tackle (the rise of anti-establishment sentiment) by making it about him; we see now that was a radical big mistake for him and now he's paying the ultimate price by having to resign much like David Cameron last June when they try to leverage that personal popular support for him on a wider canvas and ultimately it just simply failed," said Maastricht University's European Studies professor, Michael Geary, in an interview on CNBC's "Squawk Box".

Italy on Sunday cast their votes in a referendum on constitutional reforms.

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Italy's referendum on Sunday also came ahead of elections in Germany, France and the Netherlands next year, where populist parties including France's National Front are seeing growing support.

The party fervently opposes the EU and is renowned for its very conservative and nationalist views on immigration and globalization. However, Marine Le Pen has tried to soften the party's image in recent years by de-radicalizing some of its positions and expelling some more controversial members for extreme comments, including her own father.

She has also vowed to hold a referendum on France's euro and EU membership if elected.

"Just the premise alone of a referendum on euro zone membership would create a major crisis," said Stratfor's Bosoni.